M 3.3 Assignment (1)

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Broward College *

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PHY2053

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Mechanical Engineering

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Dec 6, 2023

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Name: __________________________________________ M3.3 Assignment 6 Worksheet Rotational Motion Instructions You should download this page and complete all your work directly on the worksheet. You may hand write your solutions, but you cannot receive credit for the assignment without both the solutions and the final answer. Scan and save your worksheet, together with your handwritten or typed solutions to each problem, as a .doc, .docx or .pdf or .rtf or an image file (png, jpg, jpeg or gif) file. Submit your completed work to the M3.3 Assignment 6 dropbox. See the Schedule and Course Rubrics in the Syllabus Module for due dates and grading information. 1) During a very quick stop, a car decelerates at 7.00 m/s 2 . (a) What is the angular acceleration of its 0.280-m-radius tires, assuming they do not slip on the pavement? -25 rad/s (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95.0 rad/s? 29 rev (c) How long does the car take to stop completely? 3.8 s (d) What distance does the car travel in this time? 50.54 m (e) What was the car’s initial velocity? 26.6 m/s 2) Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s 2 , what is the angular acceleration of the yo-yo? 6.8 rad/s 2 (b) What is the angular velocity after 0.750 s if it starts from rest? 5.1s (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on
its edge? 1.7 m/s 2 3) A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 30.00 rad/s 2 and her lower leg has a moment of inertia of 0.750 kg m 2 . What is the force exerted by the muscle if its effective perpendicular lever arm is 1.90 cm? 1184.21 N 4) An advertisement claims that an 800-kg car is aided by its 20.0-kg flywheel, which can accelerate the car from rest to a speed of 30.0 m/s. The flywheel is a disk with a 0.150-m radius. (a) Calculate the angular velocity the flywheel must have if 95.0% of its rotational energy is used to get the car up to speed. 321.7 rad/s (b) What is unreasonable about the result? The result is unreasonable because the calculated angular velocity of flywheel is too high. Such a high angular velocity for a car flywheel is unrealistic and it would require an enormous amount of energy that would not be available for a car. (c) Which premise is unreasonable or which premises are inconsistent? The premise that is unreasonable in this problem is the requirement for a flywheel with an angular velocity of approximately 321.7 radians per second to accelerate a car from rest to a speed of 30.0 m/s. This is unrealistic and impractical for a car's flywheel. The problem's premise assumes an unreasonably high angular velocity for the flywheel to achieve the desired result, which is inconsistent with real-world engineering constraints. 5) (a) Calculate the angular momentum of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.400kg m 2 . 15.08 kmg 2 /s (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia if his angular velocity decreases to 1.25 rev/s. 1.92 kgm 2 (c) Suppose instead he keeps his arms in and allows friction of the ice to slow him to 3.00 rev/s. What average torque was exerted if this takes 15.0 s? 0.5 Nm All Calculations Below
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